Corneal Biomechanics

Measuring corneal biomechanics in vivo

Measuring biomechanical properties clinically is currently one of the most exciting fields in modern ophthalmology. Biomechanical properties are defined as the response of a biomechanical tissue to a force. The cornea is visco-elastic which means that it exhibits both viscous and elastic biomechanical behaviour.

The applications of measuring these features in clinical practice are numerous since several diseases such as keratoconus have their origin in the change of biomechanical properties. Before corneal curvature or thickness changes due to the disease, the corneal stiffness and elasticity is already altered. Therefore, measurement of biomechanical properties is crucial for the detection of subclinical keratoconus.

A higher safety, as patients at risk for developing ectasia after LASIK can be excluded

A higher efficiency, as surgery can be performed when patients have a stiff and stable cornea

Moreover, many corneal treatments such as laser vision correction (LVC), corneal cross-linking or corneal incisions lead to an altered corneal biomechanical response which finally influences the vision of the patient.

IOP-Measurements: closer to the physiological IOP

The intraocular pressure measurement by applanation tonometry is highly influenced by the biomechanical properties. Therefore, taking biomechanical properties into consideration will provide a much more accurate IOP reading, closer to the physiological IOP. In conventional Goldman tonometry IOP readings can be completely off when the biomechanical properties of the cornea are altered – as for example after LASIK. This could lead to wrong decisions in the diagnosis and management of glaucoma.

Biomechanical properties as independent risk factors for glaucoma

Despite leading to a more accurate measurement of IOP the biomechanical properties of the eye ball are supposed to be independent risk factors for glaucoma. This allows screening for normal tension glaucoma by biomechanical parameters such as stiffness.

The biomechanical properties of the cornea can be measured by the evaluation of the response of the cornea when placed under stress. This can be achieved by an external force such as an air pulse – as done with the Corvis® ST.

Corvis® ST: Measurement Principle

The Corvis® ST is a combination of an air pulse tonometer with an ultra-high-speed Scheimpflug camera. Shortly before the air pulse starts the cornea is illuminated by a blue slit light. At this moment corneal thickness is measured as well. Afterwards the high-speed camera tracks the biomechanical response of the cornea. Within 31 ms the camera records 140 images of the horizontal sectional plane. This is a frame rate of more than 4300 images / second.

The movement of the cornea is mainly influenced by three factors which can be measured by the instrument:

Intraocular pressure (IOP)

Biomechanical properties of the cornea

Corneal thickness

All 140 images depict a complete picture of the biomechanical response of the cornea. At the beginning the cornea is in its initial convex shape. The air pulse drives the cornea backwards until the first applanation occurs. Afterwards, the cornea is further deformed until the moment of maximal concavity. After an oscillation phase the cornea returns back to its original shape. Before it reaches the initial state it passes through a second applanation, where the cornea is flat again.

During this dynamic corneal response three moments in time are of major interest:

The first applanation, when the cornea is flat.

The moment of highest concavity.

The second applanation, when the cornea is flat again before it returns to its original state.

The Corvis® ST is able to measure important Dynamic Corneal Response parameters during the whole process. The complete biomechanical response is described in detail by Cynthia Roberts.

Measurement Parameters

The Deformation Amplitude describes the movement of the apex in vertical direction. This movement depends on the overall corneal stiffness and from the intraocular pressure as well. The higher the corneal stiffness, the smaller the Deformation Amplitude. The Whole Eye Movement describes the movement of the whole eye in vertical direction. It depends on the biomechanical properties of the sclera and the fat tissue behind the eye.

The deflection amplitude describes the movement of the cornea and therefore has a stronger dependency on corneal properties. It is calculated as the difference between Deformation Amplitude and Whole Eye Movement.

DA ratio 2mm

This parameter is calculated based on the ratio between the Deformation Amplitude (vertical displacement) at the corneal apex and the Deformation Amplitude at 2 mm nasal and temporal from the apex. In case of a softer tissue the cornea starts to deform only in the center whereas the paracentral part of the cornea deforms much less. Therefore, the DAratio is higher in softer corneas than in stiffer corneas. In stiffer corneas the central and paracentral parts of the cornea are deformed at the same time and the DAratio is relatively small.

Integrated Radius

During the concave phase of the deformation the central Radius of curvature is calculated. A softer tissue exhibits a smaller radius as stiffer corneas do. The inverse Radius (1 / R) is calculated and the area under this inverse Radius vs. time curve is determined. This area is called integrated Radius and is a very good parameter to quantify the effect of corneal cross-linking. If this parameter gets smaller it indicates a stiffening of the cornea.

The biomechanical properties of the cornea are responsible for its function. Especially, the elastic properties of the cornea are responsible for the stability of the eye globe and a stable refraction as well. Elasticity is defined as the capability of a body to deform reversibly under an external force. The higher the force that is needed to deform an elastic body, the higher is the stiffness.

Analogous to a three point deformation of a beam, the bending stiffness can be defined as the ratio between applied force and the resulting vertical displacement:

Stiffness = force / displacement

In case of the stiffness parameter the load is calculated based on the difference between the strength of the air pulse at the corneal surface and the biomechanically corrected IOP (bIOP). The displacement of the corneal apex at the time point of first applanation is measured directly with the high-speed Scheimpflug camera (A1 deflection amplitude = vertical displacement at first applanation)1. The stiffness parameter is one of the best individual parameters to distinguish normal eyes from keratoconic eyes2.

Applanation tonometry and non-contact tonometry are both based on a simple principle: Applying a mechanical force on the cornea and correlation of the force that is needed to flatten the cornea with the intraocular pressure (IOP). The measured IOP values are influenced by the corneal thickness and the corneal elasticity – and therefore by corneal stiffness. Corneal stiffness is strongly changed for example in case of keratoconus but also after corneal refractive surgery. Moreover, age is known to influence the elastic biomechanical properties. These changes of biomechanical properties can lead to a larger over- or underestimation of the IOP and therefore lead to a wrong management of glaucoma.

The biomechanical corrected IOP (bIOP) takes corneal thickness, age and the biomechanical properties of the cornea into consideration. This enables an accurate IOP estimation even in case of altered biomechanical properties1.

The equation was derived based on so-called finite element simulations. In numerical simulations the influence of corneal stiffness, corneal thickness, curvature and the biomechanical properties on IOP measurements was analysed systematically. Based on these results an equation was developed that compensates for these influencing factors. Experimental and clinical studies have proven the accuracy of the bIOP. Especially after refractive surgery the bIOP is much more accurate than conventional methods for IOP measurement1.

The Corvis Biomechanical Index was developed by Riccardo and Paolo Vinciguerra from Italy, in order to detect early keratoconus based on the biomechanical response of the cornea. After a hypothesis of Cynthia Roberts, PhD and William Dupps, PhD the morphological and geometrical changes in case of corneal ectasia are only the consequence of earlier biomechanical changes. Changes of corneal curvature or pachymetric changes are therefore only secondary effects. Based on the model suggested by Dubbs and Roberts a local reduction of the elastic modulus occurs first, which causes a cycle of biomechanical decompensation leading to the well-known topographical changes1. Theoretically, corneal ectasia could be therefore first detected based on corneal biomechanical properties.

The CBI was developed solely for this purpose. It is based on a logistic regression formula including different Dynamic Corneal Response (DCR) parameters, the Stiffness Parameter and the corneal thickness profile of the horizontal sectional plane. In a large multicentre study the high accuracy of this index to distinguish normal eyes from eyes with keratoconus was proven. In this study including more than 600 eyes the accuracy was higher than 98 percent2. Moreover, the clinical use of this index in case of subclinical or forme fruste keratoconus was proven in another publication. Many of these cases could be detected by the CBI, even though no topographic or tomographic abnormalities could be observed3. These case examples support the hypothesis that biomechanical changes occur before morphological changes are present.

The detection of early or subclinical forms of corneal ectasia is gaining more attention as these cases are supposed to be at high-risk for developing iatrogenic ectasia after laser vision correction. In addition, an early detection of the disease is also important in order to perform corneal cross-linking before the vision was already affected.

Currently, screening for subclinical ectasia is mainly done by corneal tomography or corneal topography. Unfortunately, based on these methods a significant amount of cases remains unrecognized, this could represent a high risk when performing refractive surgery in these normal appearing cases. Biomechanical analysis offers a new tool to optimize the screening and to detect cases that are at high risk despite having a normal topography and normal tomography.

Prof. Renato Ambrósio from Brazil developed and index that combines tomographic and biomechanical parameters in order to reach maximal accuracy. Based on a so-called random forest algorithm – a modern machine learning approach – an overall risk score is provided to evaluate ectasia susceptibility.

A random forest algorithm consists of 500 different uncorrelated decision trees – each using tomographic and biomechanical parameters. Each tree makes a classification being either normal or ectasia based on the input variables. The TBI finally represents the percentage, how many trees the cornea classified as normal and how many as abnormal.

In a validation study this index had the highest accuracy for the detection of subclinical keratoconus compared to all other tested methods including corneal topography and tomography1. Current cross-validation from Brazil, India, Iran, Hong Kong and Germany indicate similar results.

Biomechanics: Theory and Applications

The understanding of corneal biomechanical properties is an area of intensive research over the last decade now. Several experts all over the world have contributed to the understanding of the biomechanical behaviour of the cornea. Others have worked on new methods to measure biomechanical properties in vivo or ex vivo. Corneal cross-linking has been established which is based on the alteration of the biomechanical properties. In the following section experts in the different field summarize parts of their work.

Prof. Eberhard Spoerl, PhD is one of the inventors of corneal cross-linking. Since 1993 is head of the laboratory for biomechanics in the Technical University of Dresden and is investigating the biomechanical properties of the eye ball along with testing methods to stiffen the cornea. In the following document he describes basic concepts of biomechanical properties such as the concept of elasticity and ways to measure stress strain curves ex-vivo.

Definitions

Visco-elasticity

A visco-elastic material exhibits both elastic and viscous properties. The cornea is such a visco-elastic material. Elastic properties are mainly driven by collagen fibres, the viscous properties by the matrix between the fibres consisting of proteoglycans that cause friction.

Elasticity

The capability of a body to change its shape when a force is applied and to return into its original shape when the influence of the force is removed.

Viscosity

Viscosity is often referred to as the “thickness” of a fluid. Honey for example has a much higher viscosity than water. In opposite to elastic materials viscous material are not deformed reversible when an external force is applied, but move continuously under shear or tensile stress and do not return to their original shape. Viscosity is a measure of its resistance against progressive deformation by shear stress or tensile stress. At a molecular level, viscosity is caused by the interaction or friction between molecules. The higher the friction between different layers of the material the more force is needed keep the material flowing.

Stress–strain curve

Biomechanical properties of the cornea can be measured ex vivo in tensile tests or inflation tests. The change in length can be plotted as a function of the applied force. In order to obtain properties independent from the shape of the material the change in length is normalized to the original length L0 . The ratio between change in length and original length is called strain.

Strain:

Stress:

The force is also normalized to the cross sectional area on which the fore is applied. The ratio between force and cross sectional area is called stress.

In a spring the relationship between stress and strain is linear. The cornea exhibits a hyper-elastic behaviour which means that with increasing strain more force is needed to deform the cornea.

Elastic modulus

The Elastic modulus is a measure to describe the elastic behavior independent from shape and amount of material. It describes the relationship between stress and strain. More precisely the Elastic modulus is calculated based on the slope of the stress-strain diagram. The higher the resistance of a material against the elastic deformation the higher this slopes and the higher the Elastic modulus. Stiffer materials therefore have a higher elastic modulus. In case of a tensile force the Elastic modulus is also called Young´s modulus.

Stiffness

Stiffness is a term to describe the overall rigidity of an object – it is a measure of the resistance against elastic deformation as a response to the applied force. Bending stiffness is the resistance against bending deformation. Stiffness is dependent on both the Elastic modulus which describes the intrinsic material properties and the amount of material.

Bending stiffness of a beam is calculated based on the following equation:

With F = applied force on the beam and δ vertical displacement or deflection along the same direction as the force is transferred.

Hysteresis

Hysteresis is a term describing the energy loss which is caused by a visco-elastic material due to friction. Mathematically, it can be calculated as the area between the loading and unloading curve in a stress-strain diagram. In a perfect elastic material – as in a perfect spring – no energy loss would occur until the spring returns to its original shape. Therefore, the hysteresis is zero in this case. This example illustrate the hysteresis is influenced by both viscous and elastic properties and does not reflect rigidity or material stiffness.

Vital

Biomechanics meets Tomography

Vital for the successful measurement is interaction. In that regard OCULUS set the benchmark in the market. With the Pentacam® and the Corvis® ST, interaction performs flawlessly: By combining tomographic data from the Pentacam® examination with biomechanical data from the Corvis® ST, ophthalmologists can further improve sensitivity and specificity in the detection of patients with a significant risk for developing ectasia after refractive surgery.